A bowl collects 1.67 cm height of water in its first week in a dewdrop. Each week the height of the water increases by 4% more than it did the week before. By how much does it increase in nine weeks, including the first week?
Answers
Given : A bowl collects 1.67 cm height of water in its first week in a dewdrop. Each week the height of the water increases by 4% more than it did the week before
To find : how much does it increase in nine weeks
Solution:
Height in 1st week = 1.67 cm
Height increased in 2nd week = 1.67 ( 1 + 4/100) = 1.67* 1.04 cm
Height increased in 3rd week = 1.67*1.04( 1+ 4/100) = 1.67* 1.04² cm
Height increased in 9th week = 1.67* 1.04⁸ cm
This is an GP
a = 1.67
r = 1.04
Summation of 9 terms
= 1.67 ( 1.04⁹ - 1)/(1.04 - 1)
= 17.67 cm
Height increased in 9 weeks = 17.67 cm
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